Properties

Label 465.4.c
Level $465$
Weight $4$
Character orbit 465.c
Rep. character $\chi_{465}(94,\cdot)$
Character field $\Q$
Dimension $88$
Newform subspaces $2$
Sturm bound $256$
Trace bound $1$

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Defining parameters

Level: \( N \) \(=\) \( 465 = 3 \cdot 5 \cdot 31 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 465.c (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 5 \)
Character field: \(\Q\)
Newform subspaces: \( 2 \)
Sturm bound: \(256\)
Trace bound: \(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(465, [\chi])\).

Total New Old
Modular forms 196 88 108
Cusp forms 188 88 100
Eisenstein series 8 0 8

Trace form

\( 88 q - 336 q^{4} - 12 q^{5} - 792 q^{9} + O(q^{10}) \) \( 88 q - 336 q^{4} - 12 q^{5} - 792 q^{9} + 2 q^{10} + 168 q^{11} - 116 q^{14} - 24 q^{15} + 1360 q^{16} + 392 q^{19} + 238 q^{20} - 204 q^{25} + 432 q^{26} - 1112 q^{29} - 744 q^{30} - 372 q^{31} + 64 q^{34} + 348 q^{35} + 3024 q^{36} + 624 q^{39} + 516 q^{40} + 2080 q^{41} - 4528 q^{44} + 108 q^{45} + 152 q^{46} - 4032 q^{49} - 406 q^{50} - 480 q^{51} + 2504 q^{55} + 1200 q^{56} + 1448 q^{59} - 1260 q^{60} + 56 q^{61} - 5748 q^{64} - 4256 q^{65} + 2856 q^{66} - 48 q^{69} + 282 q^{70} + 1248 q^{71} + 1952 q^{74} + 1680 q^{75} - 1724 q^{76} - 336 q^{79} + 2638 q^{80} + 7128 q^{81} - 4584 q^{84} + 4456 q^{85} - 7328 q^{86} + 4096 q^{89} - 18 q^{90} - 192 q^{91} + 3528 q^{94} - 3892 q^{95} + 5160 q^{96} - 1512 q^{99} + O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(465, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
465.4.c.a 465.c 5.b $38$ $27.436$ None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{2}]$
465.4.c.b 465.c 5.b $50$ $27.436$ None \(0\) \(0\) \(-6\) \(0\) $\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(465, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(465, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(15, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(155, [\chi])\)\(^{\oplus 2}\)